Question

find the exact value. cos 7π/3 type + or -

Explanation:

Step1: Use the cosine periodicity

The cosine function has a period of \(2\pi\), so \(\cos(x + 2k\pi)=\cos x\) for any integer \(k\).
We can write \(\frac{7\pi}{3}=2\pi+\frac{\pi}{3}\).
So, \(\cos\frac{7\pi}{3}=\cos(2\pi+\frac{\pi}{3})\).
Since \(\cos(x + 2\pi)=\cos x\), then \(\cos(2\pi+\frac{\pi}{3})=\cos\frac{\pi}{3}\).

Step2: Recall the value of \(\cos\frac{\pi}{3}\)

We know that \(\cos\frac{\pi}{3}=\frac{1}{2}\).

Answer:

\(+\frac{1}{2}\)